Polymeric drug delivery technology, which allows for medicinal ingredients to enter a cell more easily, has advanced considerably in recent decades. Innovative medication delivery strategies use biodegradable and bio-reducible polymers, and progress in the field has been accelerated by future possible research applications. Natural polymers utilized in polymeric drug delivery systems include arginine, chitosan, dextrin, polysaccharides, poly(glycolic acid), poly(lactic acid), and hyaluronic acid. Additionally, poly(2-hydroxyethyl methacrylate), poly(N-isopropyl acrylamide), poly(ethylenimine), dendritic polymers, biodegradable polymers, and bioabsorbable polymers as well as biomimetic and bio-related polymeric systems and drug-free macromolecular therapies have been employed in polymeric drug delivery. Different synthetic and natural biomaterials are in the clinical phase to mitigate different diseases. Drug delivery methods using natural and synthetic polymers are becoming increasingly common in the pharmaceutical industry, with biocompatible and bio-related copolymers and dendrimers having helped cure cancer as drug delivery systems. This review discusses all the above components and how, by combining synthetic and biological approaches, micro- and nano-drug delivery systems can result in revolutionary polymeric drug and gene delivery devices.